Supersonic wing-body interference

Citation

Abstract

A method of solving wing-body problems for circular bodies employing wings with supersonic edges has been developed. The method is based on decomposing the wing-body combination into a wing alone plus a number of Fourier component wing-body combinations corresponding to the Fourier series for the normal velocity induced at the body surface by the wing alone. The problem is then solved for each component by a method based on Laplace transform theory, and the method is then shown to be equivalent to a distributed-solution method analogous to that used by Karman and Moore to solve problems of bodies of revolution at supersonic speeds. Two sets of universal functions are presented. The first set is used to obtain the strength distribution of the fundamental solutions distributed along the body axis, from which the entire interference pressure field can be obtained. The second set permits a direct determination of the pressures acting on the body.

As an example in the use of the theory, calculations are carried out for the technologically important case of a flat rectangular wing mounted at zero incidence on a body at zero angle of attack. The calculations are carried out for four Fourier components. It was found that all four components were necessary to get good accuracy in determining the pressures at some points in the field, while only one component was required to get a fair determination of the span loading of the combination. From the example much insight into the mechanism of wing-body interference was obtained. The use of the universal functions to obtain pressures due to protuberances on nearly cylindrical bodies is discussed.